Finding Magnitudes of Forces in Similar Triangles

[afifbaha]

An upward force of magnitude 30N is combined with a second force F which makes an angle of 10degree with the horizontal. The resultant makes an anglre of 40degree with the horizontal.

a. Determine the magnitude of the second force
b. Determine the magnitude of the resultant

 

[rpthomps]

Where is your attempt?

 

[afifbaha]

Where is your attempt?

I have no idea how to do it

 

[rpthomps]

I would start with a sketch of the vectors.

 

[rpthomps]

IN fact if you make a good scale diagram, you could answer the question pretty closely and I think it would give you a good feel for the algebraic approach,

 

[afifbaha]

IN fact if you make a good scale diagram, you could answer the question pretty closely and I think it would give you a good feel for the algebraic approach,

Ok this is my diagram. Then what?

 

[rpthomps]

Well, if you made it to scale, you could just measure the lines now and that would be your answer. But if you are required to come up with an algebraic answer perhaps some trig can help you here. Can you think of some trigonometry that could help you find the sides of that shape?

 

[afifbaha]

Well, if you made it to scale, you could just measure the lines now and that would be your answer. But if you are required to come up with an algebraic answer perhaps some trig can help you here. Can you think of some trigonometry that could

help you find the sides of that shape?

How can i draw to scale if i don't know the 2nd force?

 

[rpthomps]

By using a protractor. :)

 

[afifbaha]

Wh

By using a protractor. :)

What about the length of 2nd force? The magnitude is yet to be calculated

 

[rpthomps]

As long as the angles in the triangle are all the same, it doesn't matter what the size of the triangle is, it will be similar to a triangle that I draw with the exact same angles. If I know one side, then I use a scale, we will get the same answer for the lengths. That's the "magic" of similar triangles.